Comments on Russell's Logical Atomism from James Baille. Contemporary Analytic Philosophy, Second Edition:
During his early days at Cambridge, Russell adhered to the then dominant Absolute Idealism, represented there by J.M.E. McTaggart and at Oxford by F.H. Bradley, whose Appearance and Reality (I 893) marked that movement's highest point. According to this neo-Hegelian theory, the universe constitutes a single indivisible entity, "the Absolute." To consider any part as independent of the whole was to distort that thing's nature, as the only self-subsistent entity is the Absolute itself. Bradley attempted to prove his thesis a priori by arguing that the opposing model of the universe as consisting in a multitude of independent entities, qualities, and relations was self-contradictory.
Following his friend G.E. Moore, Russell focused his attack on Bradley's theory of internal relations, which he judged to be the cornerstone of Idealism. According to Bradley, when two things enter into a relation, then this fact enters into the nature of both relata. Thus if aRb, the relation to b is internal to a's nature. A full understanding of a requires a grasp of all its relations. This leads to a monistic model of the universe as one single entity whose nature is spiritual. By contrast Russell regarded reality as consisting of a set of mutually independent entities. His theory rested on a theory of external relations. That is, he viewed relations as irreducible to facts about entities or properties.
Russell combined his logic, semantics, and epistemology into one integrated metaphysical theory known as Logical Atomism. The project was to use logical analysis to reveal the basic structure of language and hence of the world. As J.0. Urmson put it, "The shortest account of Logical Atomism that can be given is that the world has the structure of Russell's mathematical logic" (Urmson 1956, p. 6). Thus, in becoming clear on the structure of language we discover the abstract formal structure of the world. In such a language, each name would correspond to one and only one particular. At the basic sentential level there would be atomic propositions corresponding to atomic facts. Atomic propositions are constituted from objects of acquaintance with which we come into direct contact, either by perception or introspection. These propositions either ascribe a monadic property to a particular, or a relation between particulars. All other propositions are truth-functions of atomic propositions. Logical Atomism accepts a correspondence theory of truth whereby an atomic proposition is true if it corresponds to an actual situation in the world, and a complex proposition's truth-value derives from those of its constituent atomic propositions and the way in which the logical connectives combine them into the complex.
Russell didn't jump directly from Idealism into the Logical Atomism that marked his philosophically most creative phase. The Principles of Mathematics (I 903) proposed a Platonic Realist theory similar to that of Alexius Meinong, including an extremely hard-line version of a referential theory of meaning whereby every linguistic expression stood for some thing with some sort of "being," not necessarily existence in space and time.
Being is that which belongs to every conceivable term, to every possible object of thought-in short to everything that can possibly occur in any proposition, true or false, and to all such propositions themselves. Being belongs to whatever can be counted.... Numbers, the Homeric gods, relations, chimeras and four-dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them. Thus being is a general attribute of everything, and to mention anything is to show that it is. (para. 427)
One motivation for his subsequent work was to avoid such a cluttered ontology. As he said in "On Denoting," "Logic must no more admit a unicorn than zoology can; for logic is concerned with the real world just as truly as zoology, though with its more abstract and general features."
I will begin my discussion of Russell's mature work with his Theory of Descriptions, which dates from the publication of "On Denoting" in 1905. While some commentators write as if Frege and Russell had a shared theory on issues of meaning and reference, significant differences exist between them that can be traced back to Russell's empiricist leanings. Russell is not interested in logical analysis purely for its own sake. Rather, his employment of logical techniques is tied to ontological and epistemological concerns. When he translates a sentence into a more logically pellucid form, he does so to reveal the ontological commitments of the proposition expressed, about which we may be misled by the sentence's surface grammar. This project is encapsulated in his principle of logical constructionism, that "wherever possible, replace inferred entities by logical constructions."
At this point, we should bring in another strand of Russell's theory, his distinction between knowledge by acquaintance and knowledge by description. The for- mer involves direct sensory apprehension of particular sense-data, or reflective aware- ness of a universal (e.g., redness) instantiated by such a particular, whereas the latter is inherently propositional, providing information about something relative to a description. Thus, descriptive knowledge of something involves knowing certain truths about it, as so described. Russell supports the principle of acquaintance, that knowl- edge by description ultimately rests on knowledge by acquaintance: "Every proposi- tion which we can understand must be composed wholly of constituents with which we are acquainted" ("Knowledge by Acquaintance and Knowledge by Description '" 191 1, p. 219). Russell used logical analysis as a tool of ontological economy, showing that what purported to be referring expressions could be analyzed and reduced and thereby shown to be mere constructions out of objects of acquaintance.
The Theory of Descriptions is designed to solve certain puzzles regarding apparently referring expressions. To understand Russell's solution to these problems, we must be clear on three theoretical commitments that he regarded as nonnegotiable throughout his philosophical life.
• The principle of compositionality: The meaning of a sentence is a function of the meanings of its constituent parts, together with its syntactic structure.
• Classical logic, including the Law of Noncontradiction (p and -p can't both be true) and the Law of the Excluded Middle ("p or -p" is always true).
• The object theory of reference: The meaning of a referring expression is the entity it stands for.